Implementation of salt-induced freezing point depression function into

Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2018-466 Manuscript under review for journal Hydrol. Earth Syst. Sci. Discussion started: 8 October 2018 c Author(s) 2018. CC BY 4.0 License.

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Implementation of salt-induced freezing point depression function into

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CoupModel_v5 for improvement of modelling seasonally frozen soils

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Mousong Wu1,2,3, Per-Erik Jansson2, Jingwei Wu1* , Xiao Tan1,4, Kang Wang1, Peng Chen5, Jiesheng

4

Huang1

5

1.

6 7

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 430072 Wuhan, Hubei, China

2.

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Department of Sustainable Development, Environmental Science and Engineering, KTH Royal Institute of Technology, 10044 Stockholm, Sweden

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3.

Department of Physical Geography and Ecosystem Science, Lund University, 23362 Lund, Sweden

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4.

State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource

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& Hydropower, Sichuan University, 610065 Chengdu, Sichuan, China

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5.

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Abstract

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Soil freezing/thawing is important for soil hydrology and water management in cold regions. Salt in

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agricultural field impacts soil freezing/thawing characteristics and therefore soil hydrologic process. In

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this context, we conducted field experiments on soil water, heat and salt dynamics in two seasonally

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frozen agricultural regions of northern China to understand influences of salt on cold regions hydrology.

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We developed CoupModel by implementing impacts of salt on freezing point depression. We employed a

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Monte-Carlo sampling method to calibrate the new model with field observations. The new model

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improved soil temperature mean error (ME) by 16% to 77% when new freezing point equations were

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implemented into CoupModel. Nevertheless, we found that parameters related to energy balance and soil

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freezing characteristics in the new model were sensitive to soil heat and water transport at both sites.

Department of Geology, Lund University, 23362 Lund, Sweden

* Correspondence author. Email: [email protected]

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However, a systematic model sensitivity and calibration has shown to be able to improve model

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performance, with mean values of R2 from behavioral simulations for soil temperature at 5 cm depth as

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high as 0.87 and 0.90, and mean value of R2 for simulated soil water (liquid or total water contents at 5

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cm depth) of 0.31 and 0.80 at site Qianguo and site Yonglian, respectively. This study provided a new

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approach considering influences of salt on soil freezing/thawing in numerical models and highlighted the

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importance of salt in soil hydrology of seasonally frozen agricultural soils.

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Keywords: Saline soil; freezing point; seasonal frost; sensitivity; soil hydrology

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1. Introduction

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Soil freezing and thawing processes have long been recognized for its importance in not only

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engineering applications (e.g., construction of roads and pipelines) (Jones, 1981; Hansson et al., 2004;

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Wettlaufer and Worster, 2006), but also environmental issues (e.g., soil erosion, flooding, and pollutants

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migration) (Andersland et al., 1996; Seyfried and Murdock, 1997; Baker and Spaans, 1997 ; McCauley et

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al., 2002). Knowledge on soil freezing and thawing could uncover mechanisms on water and salt

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distribution in soil (Baker and Osterkamp, 1989), on frost heaving (Wettlaufer and Worster, 2006), on

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waste disposal technology (McCauley et al., 2002), as well as on climate change and water management

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in cold regions (Lopez et al., 2007).

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Laboratory and field experiments on hydrological characteristics of freezing/thawing soils have been

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conducted to understand soil hydrology in cold regions. Most of the experiments focused on soil freezing

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characteristics under various climate and soil conditions (Williams, 1964; Black and Tice, 1989; Spaans

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and Baker, 1996; Azmatch et al., 2012), regional water and energy balance in winter (Fuchs et al., 1978;

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Baker and Spaans, 1997; Hayashi et al., 2004; Watanabe et al., 2013; Zhou et al., 2014). There were very

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few studies on salt transport in frozen soils, except for frost heaving. Cary et al. (1979) found salt can

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decrease frost heaving and increase infiltration in frozen soils based on observations. Konrad and

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McCammon (1990) found the expulsion of salt from ice is dependent on freezing rate of soil. 2


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Hydrological effects of salt in cold regions have not been deeply explored. Wang et al. (2016) compared

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water and salt fluxes in two agricultural fields same as in this study, and detected different flow

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characteristics of salt during soil freezing and thawing seasons. They demonstrated that salt expulsion and

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dispersion are not negligible in frozen soils. Wu et al. (2016a) found that evaporation during winter was

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controlled by soil salt and groundwater in field frost tube experiments, in Inner Mongolia, China. They

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also demonstrated that water, heat and salt transport in frozen soils were coupled, and due to spatial

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heterogeneity of soil properties and technical difficulties in soil freezing/thawing experiments,

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measurements contained large uncertainties.

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Numerical models on soil freezing/thawing have been put forward by many. Jansson and Karlberg

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(2004) developed a coupled process-based model—CoupModel, to simulate water, heat as well as salt

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transport in frozen soil. CoupModel is a process-based model with detailed descriptions on coupled water

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and heat transport in frozen and unfrozen soils. It has shown to be one of the most robust models among

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other models taking soil freezing/thawing into account (e.g., SWAP, DRAINMOD, SWAT, HBV, VIC,

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and ATS etc). This model was developed and applied to forests (Gustafsson et al., 2004; Wu et al., 2013),

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agricultural field (Wu et al., 2011), permafrost (Zhang et al., 2012; Scherler et al., 2013) and other

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ecosystems (Okkonen and Kløve, 2011; Khoshkhoo et al., 2015).

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However, there were large uncertainties in modeling soil freezing and thawing due to the complexity

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of phase change and coupled processes. To reduce uncertainties in modeling, uncertainty analysis method

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was always introduced by combining experimental data with numerical models in calibration of the

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models for better representativeness of reality. The generalized likelihood uncertainty estimation (GLUE)

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technique (Beven and Binley, 1992) is the commonly used method for uncertainty analysis in

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environmental modeling. Instead of searching for an optimal parameter set, the GLUE method generates

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ensembles of parameter sets that show equally good performance in simulations, called ‘equifinality’ by

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Beven (2006). GLUE was performed by randomly sampling the parameter space within their ranges using

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Monte-Carlo sampling method, and then by selecting behavioral simulations using criteria applied to

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performance metrics.

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In this study, we performed experiments on water, heat and salt transport at two seasonal frost sites

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located in northern part of China. They are different in climate and in soil conditions, but are both

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important agricultural regions in northern part of China. The Hetao Irrigation District in China is a typical

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arid agricultural region suffering from soil salinization due to saline water irrigation, extensive

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evaporation, as well as soil freezing/thawing (Li et al., 2012). The Songyuan Irrigation District is a typical

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paddy rice grown region in northeastern part of China, suffering from high salinity due to over-

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development of salinized field into agricultural field (Liu et al., 2001). Soils in both regions go through

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freezing/thawing during winter and suffer from salinization in spring. These two sites are crucial in water

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resources management of China under the concept of water-saving agriculture. Wu et al. (2016b)

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performed calibration on soil water and heat transport based on one plot in the experimental field in Hetao

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Irrigation District in Inner Mongolia and found that the influences of salt on soil freezing should be taken

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into account. Wang et al. (2016) conducted field experiments and analyzed water and solutes transport

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characteristics at these two above-mentioned sites and demonstrated that salt transport in frozen soils is

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more complicated than in unfrozen soils due to diffusion and solute rejection. Thus, we developed

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CoupModel by considering impacts of salt on freezing, and applied the new model to the agricultural sites

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for modeling water, heat and salt in two seasonal frost soils. The main objective was to 1) develop

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CoupModel by considering effects of salt on freezing point; 2) identify sensitivity of parameters; 3)

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analyze uncertainty in modeling soil hydrology in seasonal frost agricultural soils.

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2. Material and Methods

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2.1 Study sites

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Experiments were conducted at two agricultural sites of northern China. One site is located in Qianguo

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Irrigation District of Songyuan, Jilin province, China (lat: 45.24o, lon: 124.60o, hereafter referred as site

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Qianguo) (Fig. 1). Field experiment at site Qianguo was conducted during 2011/2012 winter. Annual

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precipitation at site Qianguo is 451 mm and annual mean air temperature is 5.1 oC (averaged from 2011 to

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2012). This study site is typical for its soil texture classified as clay, which has a high bulk density, low

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porosity, and low hydraulic conductivity (Table 1). Soil profile at site Qianguo is homogeneous, with

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porosity of 0.46 and bulk density of 1.42 g cm-3. The water table in this area fluctuates between 1.5 and

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2.0 m. Maximum frost depth at site Qianguo is 1.2 m. Six plots (2×2 m2 for each) were selected in a

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paddy field, which was cultivated with paddy rice from May to October. On 2011/10/09, 20 mm NaBr

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solution containing 6.5 g L-1 Br- was applied to each plot to from the initial profile for Br-. Before

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spraying the solution, stubbles were removed from the plots and surface was ploughed to depth of 20 cm.

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Fig. 1 Locations of the study sites. Site Yonlian is located at the middle part of Hetao Irrigation District of

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Inner Mongolia Autonomous Region, northern part of China, site Qianguo is located at Songyuan County

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of Jilin Province, northeastern part of China.

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The other site is located at Yonglian experimental station in Hetao Irrigation District of Inner

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Mongolia Autonomous Region, China (lat: 41.13o, lon: 108.00o, hereafter referred as site Yonglian) (Fig.

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1). Field experiment at Yonglian was conducted during 2012/2013 winter from October 1st to April 30th.

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Annual precipitation at this site is 140 mm, and annual mean air temperature is 6.4 oC (averaged for

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2012~2013). Soil profile is heterogeneous, with porosity of 0.42-0.46 and bulk density of 1.44-1.53 g cm-

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to 6th of 2012, flooding irrigation (autumn irrigation) with 250 mm water was applied to the field for

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leaching salt that accumulated during growing season. Soil profile mean salt content (mainly NaCl) is 0.1%

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g g-1 for the study site, and irrigation water electrical conductivity is 0.5 mS cm-1. Before autumn

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irrigation, five plots (2×2 m2) were selected for experiment at different parts of the agricultural field, and

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ploughed to 20 cm depth.

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Table 1 Soil physical and chemical properties at two study sites Qianguo and Yonglian.

(averaged over 5 plots). Water table fluctuates between 1.5 and 3 m during winter. From November 4th

Clay (%)

Silt (%)

Sand (%)

Organic matter (%)

Bulk density (g/cm3)

Porosity (-)

0-140

32.40

38.40

29.30

1.76

1.42

0.46

0-10

27.91

17.20

54.89

0.53

1.49

0.44

10-20

37.46

21.65

40.90

1.08

1.45

0.45

20-30

31.69

48.39

19.92

0.77

1.44

0.46

30-40

34.08

34.32

31.61

0.73

1.45

0.45

40-60

28.74

34.85

36.40

0.53

1.47

0.45

60-80

34.67

30.45

34.88

0.77

1.45

0.45

80-100

17.65

18.46

63.88

1.14

1.53

0.42

100-140

14.81

35.05

50.15

0.44

1.53

0.42

Site

Depth (cm)

NE

IM

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2.2 Experimental design

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TDR probes (Model: CS605, Campell Scientific Inc.) were installed at site Qianguo to detect liquid

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water content. Due to difficulty in long-term maintaining of TDR system in rural regions, only daily

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liquid water was manually recorded with a datalogger (TDR 100; Campbell Scientific Inc.). TDR probes

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were calibrated in laboratory with unfrozen soil, and the precision of calibration was maintained with R2

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of 0.97. TDR probes were then inserted horizontally into the soil pit (10 m apart from the experimental

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plots) from 5 cm to 100 cm depth with 10 cm interval. PT100 temperature sensors were installed at the

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same depth as TDR probes, and the daily temperature data were collected.

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During soil freezing/thawing season at site Qianguo, 7 sampling dates were chosen (2011/10/09,

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2011/11/09, 2011/11/25, 2011/12/20, 2012/02/15, 2012/04/10, 2012/04/20), and soil samples from 0 to

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100 cm with 10 cm interval were collected for determining total water content and Br- content. An electric

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drill (5 cm in diameter, 10 cm in length) was used for sampling frozen soil for every 10 cm depth. Total

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water content was determined by oven-dry method. Br- content was determined by diluting 50 g wet soil

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into 250 mL deionized water, and measuring the electrical potential (mV) using an electrical potential

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meter (MP523-06). Then the electrical potential was converted into Br- concentration by a pre-calibrated

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relationship between Br- concentration and electrical potential (calibration R2=0.99). Soil temperature and

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liquid water content at 4 depths (5, 15, 25, and 35 cm) from site Qianguo were used to calibrate

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CoupModel, while soil water storage and salt storage at various depths (0-10 cm, 0-40 cm, 0-100 cm)

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estimated form soil profile samplings were used to validate the model.

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Total water content and Cl- content from 0 to 100 cm with 10 cm interval at site Yonglian were

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sampled at 14 dates from October 2012 to April 2013 (2012/10/16, 2012/10/27, 2012/11/10, 2012/12/04,

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2012/12/15, 2012/12/26, 2013/01/05, 2013/01/14, 2013/01/25, 2013/03/05, 2013/03/14, 2013/03/25,

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2013/04/07, 2013/04/18). The sampling and measurement methods for total water content and Cl- content

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were the same as those at site Qianguo. During experimental period (2012/10/01-2013/04/30), hourly soil

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temperatures at 5, 15, 25 and 35 cm depth were recorded by the PT100 temperature sensors from the

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micro-meteorological station in the field. Groundwater table depth was measured every day during the 7


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autumn irrigation and drainage period (2012/11/4 to 2012/11/15), and for every five days during the rest

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time of the winter. Soil started freezing from November 12th, 2012, and total thawed on April 30th, 2013.

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Measuring of groundwater table depth was conducted manually by putting a roped copper cup into

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observation well, and then measuring the rope length when the cup touched water (by hearing the voice).

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Soil temperature, soil total water content at 4 depths (5, 15, 25 and 35 cm) and groundwater table depth

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were used to calibrate CoupModel, while water storage and salt storage at different depths (0-10 cm, 0-40

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cm, 0-100 cm) estimated from soil profile samplings were used to validate the model.

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Meteorological data e.g. air temperature, humidity, radiation, wind speed, and precipitation, were

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obtained from the nearest meteorological station at each site with hourly-resolution from October 1st,

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2011 to April 30th, 2012 and from October 1st, 2012 to April 30th, 2013 at site Qianguo and site Yonglian,

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respectively.

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3. CoupModel_v5

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Model domain covered from soil surface to 6 m depth, with unit area considered. Soil profile was

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discretized into 16 layers, with 10 cm thickness each layer from 0 to 40 cm, 20 cm thickness from 40 cm

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to 2 m, and 1 m thickness from 2 m to 6 m. Input meteorological data were hourly, and model time step

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was set as hourly. Numerical solution of water, heat and salt transport in soils was based on forward

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difference method. Model performance metrics on different output variables was calculated automatically

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using modules implemented into CoupModel_v5. Major model processes considered in this study were

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described in the following sections.

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3.1 Soil water processes

166 167

CoupModel solved coupled differential equations for water and heat transfer (Jansson, 2012). Water flow in the soil matrix was described by Richards equation: ∂θ ∂ = ⎡kw ∂t ∂z ⎣

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(

∂ψ ∂z

∂ ⎛ ∂C ⎞ ∂q − 1 ⎤⎦ + ⎜ Dv v ⎟ − bypass ∂z ⎝ ∂z ⎠ ∂z

)

8

(1)


θ

is water content (m3 m-3); k w is hydraulic conductivity (m s-1); ψ is matric potential (m); Dv is

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where

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vapor diffusion coefficient (m2 s-1);

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pores (m s-1);

172 173

z

Cv is vapor density (m3 m-3); qbypass is the bypass flow in macro

is depth to soil surface (positive downward) (m); and t is time (s).

Vapor flow (second term inside brackets on right side of Equation (1)) in soil was determined by vapor gradient between two layers and diffusion coefficient, adjusted by tortuosity 𝑑!"#$ (Equation (2)).

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𝑞! = 𝑑!"#$ 𝐷! 𝑓!

!!!

(2)

!"

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where 𝑑!"#! is a parameter accounting for tortuosity; 𝐷! is the diffusion coefficient for free air (m2 s-1);

176

𝑓! is the soil air content (m3 m-3); 𝐶! is vapor density (m3 m-3); and 𝐷! is vapor diffusion coefficient (m2 s-

177

1

).

178

The diffusion coefficient for free air, 𝐷! was a function of soil temperature (Equation (A1) in Table

179

A2), and vapor density 𝐶! was calculated from vapor pressure (Equation (A1)), which was estimated

180

from soil matric potential and soil temperature (Equation (A1)).

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Infiltration through frozen soil was estimated separately for the low- and high-flow domains (Stähli et

182

al., 1996). CoupModel took the preferential flow in macropores into account using a bypass routine when

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excess water entering the soil was routed directly to the next underlying soil layer through the high-flow

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domain (Jansson, 2012). Infiltration into soil was determined by the soil adsorption rate adjusted by a soil

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matric water adsorption coefficient 𝑎!"#$% (Equation (5)). When infiltration water was larger than soil

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adsorption rate, bypass flow would occur. Bypass flow in macro pores was determined by

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𝑞!"#$%% =

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𝑞!"# =

0 𝑞!" − 𝑞!"#

max 𝑘! 𝜃 𝑠!"#

!" !"

1 < 𝑞!" < 𝑠!"# 𝑞!" ≥ 𝑠!"#

+ 1 , 𝑞!"

𝑞!" ≥ 𝑠!"#

9

1 < 𝑞!" < 𝑠!"#

(3)

(4)


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𝑠!"# = 𝑎!"#$% 𝑎! 𝑘!"# 𝑝𝐹

(5)

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where 𝑠!"# is soil adsorption rate (m s-1); 𝑎!"#$% is soil matric water adsorption coefficient, 𝑎! is a

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geometry coefficient to describe thickness ratio to horizontal scale of each soil layer; 𝑘!"# is matric

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maximum hydraulic conductivity (m s-1); and 𝑝𝐹 is pF value of soil.

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Flow in low-flow domain obeyed Darcy’s law and soil water retention curve was determined by

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Brooks and Corey (1964) equation (Equation (A3)), with the air entry at different layers to be adjusted in

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calibration. Hydraulic conductivity in low-flow domain was calculated from the Mualem (1976) equation

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(Equation (A4)). In frozen soil, hydraulic conductivity was modified for high-flow (Stähli et al., 1996).

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In high-flow domain, water flow was modeled by gravitational flow under unit gradient, and hydraulic

198

conductivity was adjusted by using impedance factor 𝑐!,! in high-flow domain (Equation (6)):

199

k fh = e

−

θi cθ ,i

(k

w

(θtot ) − kw (θlf + θi ))

(6)

200

where kw (θtot ) is hydraulic conductivity for pores saturated with water (m s-1); k w (θlf + θi ) is hydraulic

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conductivity when water flow in low domain with ice existence (m s-1); θi / cθ ,i is reduced factor; cθ ,i is

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impedance factor; 𝜃!"! is total water content in high- and low-flow domains (m3 m-3); 𝜃!" (=𝑑! 𝜃!"#$ ,

203

Equation (18)) and θi (

204

thickness, m, 𝜌!"# is ice density, kg m-3) are the liquid water and ice content, respectively, in the low-flow

205

domain (m3 m-3).

!!! !!"! !!"#

, E is soil heat, J, H is sensible heat, J, Lf is latent heat, J kg-1, Δ𝑧 is soil

206

The hydraulic conductivity changed at the freezing front under partially frozen conditions. To prevent

207

excessive water redistribution towards the freezing front, the hydraulic conductivity of partially frozen

208

layers was adjusted by considering ice content influences on water flow using a factor 𝑐!" (Equation (7)).

kwf = 10

209

− c fiQ

kw

10

(7)


210

where c fi is impedance factor; and Q is heat quality, as a ratio of ice content to total water content.

211

Meanwhile, the influence of soil temperature on soil hydraulic conductivity was considered, using a

212

linear increase factor 𝑟!!! and a minimum conductivity 𝑘!"!"# to adjust hydraulic conductivity at 20 oC

213

(Equation (A7)).

214

Surface ponding of water may occur if the soil infiltration capacity was exceeded, otherwise the

215

infiltration rate was equal to precipitation and rates of snowmelt. If infiltration capacity was exceeded,

216

excess water will be transferred to the surface pool. The overland flow from surface pool was estimated

217

by the difference between surface water storage and maximum surface pool, 𝑤!"#$ (Equation (8)).

218

qsurf = asurf (Wpool − wpmax )

(8)

219

where asurf is an empirical coefficient, Wpool is the total amount of water in the surface pool (m), and wpmax

220

is the maximal amount of water stored on soil surface without causing surface runoff (m).

221

Drainage systems at two study sites were open drainage ditches, drainage at study sites was then

222

calculated by Hooghoudt equation combined with an empirical drainage equation to constitute a manual

223

drainage system, adjusted by initial drainage level 𝑧! and minimum drainage level, drain spacing 𝑑!

224

(Equation (A9)), empirical groundwater level peak value 𝑧! , and empirical groundwater flow peak value

225

𝑞! (Equation (A10)). Meanwhile, initial groundwater level was set for calibration. Groundwater water

226

level was estimated by the soil saturation layer depth to surface.

227

3.2 Soil heat processes

228 229

Heat flow in soil was described by the heat transport equation, considering conduction, convection and latent heat flow: !(!")

230

!"

− 𝐿! 𝜌!

!!! !"

=

! !"

𝑘!

!" !"

− 𝐶!

11

! !! ! !"

− 𝐿!

!!! !"

(9)


231

where C is soil (containing solid, water, and ice) heat capacity (J m-3 oC-1); T is temperature (oC); L f is

232

latent heat of freezing (J kg-1); ρ i is density of ice (kg m-3); θi is ice content (m3 m-3); kh is thermal

233

conductivity soil (W m-1 oC-1); qw is water flux (m s-1); Lv is latent heat of vaporization (J kg-1); and qv

234

is vapor flux (m s-1).

235

Upper boundary for soil heat flow was soil temperature at surface, calculated by the energy balance

236

scheme described in Section 3.4. Lower boundary for soil heat flow was controlled by soil temperature

237

fluctuation at 6 m depth, which was estimated using an analytical solution for soil heat conduction.

238

Soil thermal conductivity for both frozen and unfrozen soils was calculated from the Ballard & Arp

239

equation (Balland and Arp, 2005), adjusted by three empirical coefficients 𝛼, 𝛽, and 𝑎 (Equation (A11)).

240

Thermal conductivity from the top frozen soil layer was then corrected by using a damping function,

241

adjusted by the maximum damping coefficient 𝐶!" (Equation (A12)). When infiltration water passed the

242

high-flow domain, it would refreeze due to low soil temperature in frozen soils. Meanwhile, latent heat

243

released from refreezing would melt water in high-flow domain. This would lead to redistribution of

244

water between low-flow and high-flow domains. CoupModel considered the water redistribution and

245

adjusted it by a heat transfer coefficient 𝛼! (Equation (A13)).

246

3.3 Salt tracer processes

247 248

Salt in CoupModel was simulated as a tracer migrating with water, neglecting diffusion. Salt transport was simulated as Cl- transport in soil for estimate of salt tracer flux. Salt balance in soil is calculated as: !!!"

249

!"

=−

! !"

𝑞!"# 𝑐!" −

! !"

𝑞!"#$%% 𝑐!"#

%$(10)

250

where cCl is concentration of Cl- (kg m-3); 𝑐!"#$% is salt deposition concentration (kg m-3); 𝑞!"# is water

251

flux (m s-1), 𝑞!"#$%% is bypass flow (m s-1).

12


252

Soil salt concentration for each layer was then calculated by

253

𝑐!" (𝑧) =

!!" (!)(!!!!"# (!)) !(!)!!

(11)

254

where 𝑠!" is salt amount at each soil layer (kg m-2); 𝑠!"# is salt adsorption rate; 𝜃 is soil water content at

255

each layer (m3 m-3); Δ𝑧 is soil layer thickness (m).

256

Salt at surface was balanced by salt in precipitation and irrigation, as well as salt loss from surface

257

runoff. Lower and lateral boundaries for salt transport were salt leaching to groundwater, which was

258

proportional to drainage rate. Initial salt concentration 𝑐!" , precipitation salt concentration 𝑐!"#$% ,

259

irrigation salt concentration 𝑐!"#$$#% , as well as salt adsorption coefficient 𝑠!"# at different depths were set

260

as calibration parameters. At site Qianguo, Br- transport was converted to Cl- transport in the simulation

261

in the validation of salt storage, Cl- storage at site Qianguo was then converted to Br- storage in

262

comparison with field observations of Br- storage.

263

3.4 Energy balance processes

264 265

Surface temperature and evaporation was calculated using energy balance method, with net short-wave radiation balanced by latent heat, sensible heat and soil heat flux at surface:

266

𝑅! = 𝐿! 𝐸! + 𝐻! + 𝑞!

(12)

267

where Lv Es is the sum of latent heat flux (J m-2 s-1); H s is sensible heat flux (J m-2 s-1) and qh is heat flux

268

to the soil (J m-2 s-1).

269

Latent heat was calculated as below,

270

Lv Es =

ρ a c p ( esurf − ea ) γ ras

13

(13)


271

where ras is the aerodynamic resistance (m-1); esurf is the vapor pressure at the soil surface (Pa or in m

272

water); ea is the actual vapor pressure in the air (Pa or in m water); ρ a is the air density (kg m-3); c p is the

273

heat capacity of air (J kg-1 oC-1); Lv is the latent heat of vaporization (J kg-1) and γ is the psychometric

274

constant.

275

Sensible heat was calculated as

276

𝐻! = 𝜌! 𝑐!

(!! !!! ) !!"

(14)

277

where Ts is the soil surface temperature (oC); Ta is the air temperature (oC); and ras , ρ a , c p are the same as

278

Equation (13).

279

Soil surface heat flow was then calculated,

280

𝑞! = 𝑘!

(!! !!! ) !!! !

+ 𝐿𝑞!,!

(15)

281

where kh is the thermal conductivity of the topsoil layer (W m-1 oC-1); Ts is the soil surface temperature

282

(oC); T1 is the middle of uppermost soil compartment temperature (oC); Δz1 is the depth of the uppermost

283

soil compartment (m) and Lqv , s is the latent water vapor flow from soil surface to the central point of the

284

uppermost soil layer (J m-2 s-1).

285

Surface temperature was then adjusted to make Equation (5) balanced by different fluxes at surface.

286

Soil surface vapor pressure was determined by soil surface temperature, water potential at top layer and

287

soil water gradient between soil surface and top layer. This was further corrected by an empirical factor,

288

which was adjusted by an adjustment coefficient 𝜓!" , and the surface water balance (Equation (A14)),

289

which was adjusted by maximum soil surface water deficit 𝑠!"# and maximum soil surface water excess

290

𝑠!"#!$$ (Equation (A15)).

14


291

Aerodynamic resistance for stable atmosphere was calculated using the Richardson equation. Then the

292

aerodynamic resistance for stable atmosphere was adjusted by the momentum roughness length of soil

293

and snow surface 𝑧!! (𝑧!!,!"#$ ) (Equation (A16)), and the heat roughness length of surface 𝑧!! was

294

derived from 𝑧!! and 𝑘𝐵 !! (Equation (A17)). In addition, when surface was at extreme stability

295

!! conditions, aerodynamic resistance was then adjusted by using a windless exchange coefficient 𝑟!,!"#

296

(Equation (A18)).

297

Soil evaporation was adjusted by maximum soil water condensation rate 𝑒!"#,!"#$ considering the

298

influences of condensation of water on evaporation (Equation (A19)). Net radiation was estimated by

299

Konzelmann equation with two formulae to calculate longwave radiation and was adjusted by an

300

empirical coefficient 𝑟!! (Equation (A20)). Snow melting was determined by solving energy balance

301

equation in snowpack using the same scheme as soil surface energy balance calculation. Snow mass

302

balance was then estimated based on temperature change in snowpack as well as snow age. Snow thermal

303

conductivity was calculated from snow density with an adjustment factor 𝑠! (Equation (A21)). Soil

304

albedo was determined by albedo of dry and wet soils, adjusted by an empirical coefficient 𝑘! (Equation

305

(A22)). Snow albedo was determined by snow age, as well as cumulative air temperature since the latest

306

snowfall, adjusted by the minimum snow albedo 𝑎!"# (Equation (A23)).

307

3.5 Soil freezing point depression function development

308

To solve the coupled water and heat flow equations, we needed a relation between soil temperature

309

and soil liquid water, i.e. soil freezing characteristics. In frozen soil, when soil temperature was below

310

zero, latent heat changed due to ice formation. When soil temperature continued decreasing, sensible heat

311

also changed. In CoupModel, we assumed that soil is totally frozen when temperature was below 𝑇! (-5

312

o

313

C), when soil temperature was between 0 and 𝑇! , sensible heat in soil was calculated as:

𝐻 = 𝐸(1 −

!! !!∆!!! !!"#$ !! !!

15

)(1 − 𝑟)

(16)


314

where 𝐸 is total heat stored in soil (J); 𝐿! is latent heat of freezing (J kg-1); 𝑤 is water stored in soil (kg);

315

∆𝑧 is soil thickness (m); 𝑑! is a factor accounting for the fraction of unfrozen water to soil wilting point

316

water content; 𝜃!"#$ is the wilting point water content when the pF value of soil water is 4.2 (m3 m-3); 𝜌!

317

is density of water (kg m-3); 𝐸! is energy when soil is totally frozen (𝐶! 𝑇! − 𝐿! 𝑤!"# , i.e. when soil

318

temperature is 𝑇! , 𝐶! is heat capacity of frozen soil, J kg-1 oC-1); 𝑟 is freezing point depression.

319

In modeling of soil frost, when soil was totally frozen at -5 oC, the liquid water content was

320

determined by wilting point of soil (∆𝑧𝑑! 𝜃!"#$ 𝜌! ), and adjusted by a coefficient 𝑑! , as depicted in

321

Equation (16). Ice content in soil was calculated as:

322

!!! ,𝑇 !!!! !!"# !

0, 𝑇 > 𝑇!

𝜃! =

< 𝑇 ≤ 𝑇!

(17)

𝜃 − 𝑑! 𝜃!"#$ , 𝑇 ≤ 𝑇! 323

where 𝐸 is total energy stored in soil (J); 𝐻 is total energy stored in soil (=𝐶! 𝑇, J); 𝐿! is latent heat of

324

freezing (J kg-1); ∆𝑧 is soil thickness (m); 𝑑! is a factor accounting for the fraction of unfrozen water to

325

soil wilting point water content; 𝜃!"#$ is the wilting point water content when the pF value of soil water is

326

4.2 (m3 m-3); 𝜌!"# is density of ice (kg m-3).

327

In CoupModel, the freezing-point depression was related to soil heat storage as below:

⎛ E r = ⎜1 − ⎜ E f ⎝

328

λ

⎞ ⎟⎟ ⎠

d2λ + d3

⎛ Ef − E ⎞ min ⎜ 1, ⎜ E + L w ⎟⎟ f f ice ⎠ ⎝

(18)

329

where d 2 , d 3 are empirical constants;

330

freezing, kg, i.e. (𝑤 − ∆𝑧𝑑! 𝜃!"#$ 𝜌! ) in Equation (18); 𝐸! is soil heat storage when soil temperature is 𝑇!

331

(𝐶! 𝑇! − 𝐿! 𝑤!"# ), J.

is the pore size distribution index; 𝑤!"# is water available for

16


332

In saline frozen soil, ice formation does not start at 0 oC, but below 0 oC. Freezing point T0 (Equation

333

(19)) is a parameter related to soil type, salt type and salt content. In CoupModel, T0 was assumed as 0 oC,

334

which was not suitable for saline soils. In this study, two methods were implemented to consider salt

335

influences on freezing point depression. The first one was to set freezing point T0 as a parameter in the

336

model, and this parameter could be determined by experiments on freezing point of different saline soils.

337

The second method was to relate T0 to osmotic potential (Equation (19)). According to Banin and

338

Anderson (1974), the relationship between freezing point and salt solution could be written as below:

339

T0 = −10−4+ sc ×

π

(19)

1.221

340

where T0 is the freezing point (oC); π is osmotic potential (in unit cm); sc is a scale factor for

341

considering the influences of salt types on the relationship (range from -2 to 2); -4 is a constant for

342

converting osmotic potential unit from cm to MPa.

343

Soil salt and soil heat and water transport as well as soil freezing/thawing was connected by Equation

344

(19) with osmotic potential π, and freezing point would change as soil temperature and soil salt

345

concentration changed during simulation, since osmotic potential was determined by both soil

346

temperature and salt concentration:

347 348 349

350

𝜋 𝑧 = 𝑅(𝑇 + 273.15)

!!" (!) !!"

(20)

where R is gas constant; T is soil temperature (K); cCl is salt concentration (kg m-3); MCl is mole mass of Cl (35.5 g mol-1). 3.6 Calibration approach

351

The sensitivity analysis and model calibration procedures are summarized in Fig. 2. We selected 58

352

parameters that have either shown a large influence on modeled water and heat dynamics in previous 17


353

studies and/or are known to be important in sensitivity analysis (cf. Gustafsson et al., 2001; Wu et al.,

354

2011; Metzger et al., 2015). The 58 parameters represented the major processes related to soil water, heat,

355

radiation as well as salt transport, 19 related to soil water process, 8 related to soil heat process, 19 related

356

to soil salt process, and 12 related to energy balance process (Table A1). We noted that 58 parameters

357

made the calibration very inefficient, since some of the parameters were assigned to different layers and

358

some were not so sensitive in comparison with others. We thus conducted a two-step calibration, with the

359

first step to find out the most important parameters from different model processes based on sensitivity

360

analysis, and the second step to calibrate the important parameters.

361

In the first step, the 58 parameters were tested for each site with 70000 simulations based on Monte

362

Carlo sampling method. Each of the simulations was run with randomly selected parameter values, thus

363

creating 70000 realizations. The most sensitive model parameters were then identified for each site based

364

on their relative importance on performance metrics (e.g. R2, determination coefficient between

365

simulation and observations, and ME, the mean deviations between simulation and observations). This

366

was done by using the LGM (Lindeman, Gold and Merenda) method (Lindeman et al., 1980) that

367

averages the sequential sums of squares over all orderings of regressors, which calculates the relative

368

importance of each parameter on model performance metrics and ranks them. Based on the ranking of

369

parameters, 8 to 11 sensitive parameters (i.e. 3 common parameters for two sites, another 5 for site

370

Qianguo and another 8 for site Yonglian) were then selected in the second step with 10000 simulations

371

for each site. It is important to note that the sensitive parameters may be different from site to site

372

depending on site-specific characteristics, although initial parameters and their ranges were equivalent for

373

all sites.

18


374

Fig. 2 Model sensitivity analysis and calibration procedures. Step 1 denotes procedures for selecting

375

important parameters with LGM method, step 2 represents model calibration and selection of acceptable

376

simulations.

377

From the 10000 simulations of the second calibration step, ensemble of parameter sets for each site

378

was then selected based on statistical performance metrics (determination coefficient R2 and mean error

379

ME) for temperature and water at several depths (Table 2). In addition to useful information about site-

380

specific processes and their representations in the model, the ensemble simulation results (9 for site

381

Qianguo, 16 for site Yonglian) simulated using accepted parameter sets were used for analysis water,

382

energy and salt balance over the simulation period.

383

Table 2 Criteria applied to model performance metrics in selection of behavioral simulations. Site name Soil depth 5cm

384 385

Qianguo R

2

Yonglian ME

T

θ

R

2

ME

o

o

T ( C)

θ (%)

T

θ

T ( C)

θ (%)

[0.85,1]

[0.3,1]

[-1,1]

[-5,5]

[0.9,1]

[0.5,1]

[-0.5,0.5]

[-3,3]

15 cm

[0.9,1]

[0.8,1]

[-0.5,0.5]

[-5,5]

[0.9,1]

[0.5,1]

[-0.5,0.5]

[-3,3]

25 cm

[0.9,1]

[0.5,1]

[-0.5,0.5]

[-3,3]

[0.9,1]

[0.5,1]

[-0.5,0.5]

[-3,3]

35 cm [0.85,1] [0.7,1] a GWTD / / a GWTD is ground water table depth b unit for GWTD is m

[-0.5,0.5] /

[-2,2] /

[0.9,1]

[0.5,1] [0.6,1]

[-0.5,0.5]

19

b

[-3,3] [-0.1,0.1]


386 387

4. Results and Discussion

388

4.1 Freezing point depression

389

In Fig. 3 and Fig. 4, the sensitivity of model to freezing point depression is analyzed at 5 cm depth

390

(the same was done for other soil depths, not shown here), based on model results from one of the

391

behavioral simulations at each site. The influences of freezing point on soil heat are obvious (Fig. 3).

392

When soil freezing temperature changed from 0 oC to below zero, the relationship between soil

393

temperature and soil heat storage changed accordingly. The model performance was improved when

394

freezing point depression was related to soil salt. Mean error (ME) for soil temperature at 5 cm depth

395

decreased from 1.25 oC to 0.29 oC (improved by 77%) at site Qianguo, and from 2.54 oC to 1.83 oC

396

(improved by 28%) at site Yonglian, when freezing point decreased from 0 oC to -3 oC.

397

Fig. 3 Relationships between soil temperature and soil heat storage derived from modeling for different

398

freezing points at 5 cm depth at a) site Qianguo and b) site Yonglian.

399

The relationships between soil temperature and soil heat storage at 5 cm depth were different when

400

various 𝑠𝑐 values were assigned (Fig. 4). This indicated that different types of salt also influence soil

401

freezing/thawing. Meanwhile, ME decreased from 1.35 oC to 0.64 oC (improved by 53%) when 𝑠𝑐

402

changed from 0 to 1 at site Qianguo. At site Yonglian, ME decreased from 2.54 oC when 𝑠𝑐 is 0 to 2.14

20


403

o

404

salt content, but also the salt type should be taken into consideration for reducing uncertainty in modeling

405

soil temperature.

406

Fig. 4 Relationships between soil temperature and soil heat storage derived from modeling for different sc

407

values at 5 cm depth at a) site Qianguo and b) site Yonglian.

408

4.2 LGM relative importance in calibration parameters

C (improved by 16%) when 𝑠𝑐 was 1. This indicated that in determination of freezing point, not only the

409

At site Qianguo, for soil temperature R2 at 4 depths (Fig. 5 a)-d)), 𝑧!",!"#$ (momentum roughness

410

length of snow), which is to estimate surface aerodynamic resistance, was found to be most important.

411

This parameter would influence surface energy balance and eventually impact heat transport in soil

412

profile. The other important parameter for soil temperature R2 at 15, 25 and 35 cm depths was 𝐶!" , which

413

is a parameter to adjust thermal conductivity of surface frozen layer. For liquid water content R2 at 4 depths (Fig. 5 e)-h)), the most important parameters were 𝑧!!,!"#$ ,

414 415

!! 𝑟!,!"# , 𝑑! and 𝜓! of different depths that were related to energy balance and soil heat and water transport.

416

𝑧!!,!"#$ was already detected to be important for soil temperature. This indicated that surface energy

417

balance in snowpack at site Qianguo is important for both soil heat and water transport.

418

21


2

2

T5cm _R 31.06 %

67.70 % 0.26%

21.10 % 2.10% 61.53 %

z0M,snow d1 0.62% z p 0.36% c Cl others 2

0.23%

T15cm _R f)

b)

T5cm _ME

θ5cm _R

19.93 % 8.44%

z0M,snow Cmd 15.05 Ψ a(1) % s adc(8) others 2

1.32%

70.03 %

0.23%

58.63 %

0.21%

d)

4.97% z0M,snow Cmd Ψ a(3) s adc(5) others 2 T _R

60.84 %

16.62 %

-1

65.92 % 0.27%

6.91% z0M,snow Cmd 0.35% Ψ a(3) s adc(4) others

60.26 %

16.98 % 5.81%

z0M,snow 1.26% Cmd Ψ a(3) s adc(8) others

60.24 % 0.32%

65.50 %

16.65 r a,m ax-1 % d1 Ψ a(2) s adc(6) others

θ35cm_ME

14.26 % 2.93%

10.74 %

17.10 r a,m ax-1 % d1 0.67% Ψ a(3) s adc(4) others

θ25cm_ME

21.98 %

8.83% 62.19 %

0.33%

T35cm_ME p)

2

12.69 % 9.28%

21.72 %

12.71 -1 r a,m ax % d1 Ψ a(2) s adc(6) others

61.29 %

T25cm_ME o)

θ35cm_R l)

h)

z0M,snow Cmd Ψ a(3) s adc(8) others

10.93 %

8.05%

21.63 %

r a,m ax d1 Ψ a(2) s adc(1) others

0.19%

35cm

0.97%

2

16.70 % 5.64%

2.85%

θ15cm_ME

17.63 %

0.27%

θ25cm_R k)

28.42 %

63.53 %

68.13 %

2

T25cm _R g)

c)

10.14 %

r a,m ax-1 d1 Ψ a(1) s adc(8) others

13.24 % 0.41%

-1 19.52 r a,max d1 % Ψ a(1) 0.23% s adc(6) others

20.49 %

12.20 % 63.50 %

58.00 %

T15cm_ME n)

15.52 %

3.03% z0M,snow Cmd 2.82% Ψ a(3) s adc(2) others

s k Cmd Ψ a(1) c Clirrig others

0.28%

θ15cm_R j)

30.41 %

θ5cm_ME

7.07% 15.17 %

1.52% z0M,snow Cmd Ψ a(3) 0.26% s adc(8) others

52.51 % 0.35%

-1 29.95 r a,m ax d1 % Ψ a(3) s adc(6) others

419

Fig. 5 Relative importance for parameters to R2 a)-h) and ME i)-p) of soil temperature and soil water at 4

420

depths (5, 15, 25, 35 cm) at site Qianguo. Parameters shown in each sub-figure are the most important

421

parameter from each group, i.e. energy balance, soil heat, soil water, soil salt, and the other parameters.

422

For soil temperature ME at site Qianguo (Fig. 5 i)-l)), important parameters were similar to soil

423

temperature R2, except at 5 cm depth, with 𝑠! showing the greatest importance (Fig. 5 i)). 𝑠! is for

424

estimate of snow thermal conductivity, and determines energy balance in snowpack. Site Qianguo was

425

covered by snow during soil freezing, thus accurate estimates of snow energy balance would help in

426

improving model performance on soil temperature. At site Qianguo, important parameters for soil liquid

427

!! water content ME were similar to R2, showing that parameters related to surface energy balance (𝑟!,!"# ),

428

soil freezing characteristics (𝑑! ) and soil water characteristics (𝜓! ) have great importance to soil water

429

transport.

22


5.05%

24.42 %

14.20 %

3.32% 4.25%

66.90 %

68.77 %

-1

ra,m ax α Ψa (2) sadc (7) others

1.10%

41.80 %

KB d1 Ψa (1) sadc (8) others

62.65 %

1.18%

c)

13.17 % ra,m ax-1 0.59% αh Ψa (2) sadc (7) others 3.37% 14.63 %

58.42 %

70.58 %

5.70%

ra,m ax-1 1.17% Cmd Ψa (1) sadc (7) others

0.37%

55.55 %

3.79% 1.19%

2.22%

ra,m ax-1 Cmd Ψa (3) sadc (8) others


2.35%

ra,m ax-1 Cmd Ψa (5) sadc (6) others 2

4.19%

GWTD_R 3.08%

0.51%

6.09% 29.67 %

60.47 %

-1 9.15% ra,m ax Cmd Ψa (2) sadc (7) others

0.55%

2.36%

7.81%

9.19%

ra,m ax-1 Cmd Ψa (8) cClirrig others

3.15%

34.63 %

54.07 %


s def d1 Ψa (4) sadc (3) others

0.34%

r)

3.09%

75.53 %


θtot35cm _ME

41.07 %

30.66 % 61.55 %

θtot25cm _ME

3.22%

T35cm _ME q)

0.62%


0.28%

12.64 % 0.39%

i)

0.62%

46.75 %

4.29%

5.50%

5.95%

71.55 %


T25cm _ME p)

θtot35cm_R m)

64.85 %

9.12%

41.35 %

17.82 %

33.97 %

θtot15cm _ME

3.07%

46.52 %

2

2

T35cm_R h)

d)

0.63%

9.09% s def 0.08% d1 Ψa (8) sadc (7) others

19.14 %

11.05 %

6.11%

-1 ra,m ax Cmd 8.84% Ψ (2) a sadc (7) others

41.79 %

2 θtot25cm_R l)

2 T25cm_R g)

28.59 %

9.52% 62.59 %

T15cm _ME o) 46.24 %

6.33%

ra,m ax-1 d1 Ψa (1) sadc (7) others

2.16%

2 θtot15cm_R k)

1.94% 6.09%

0.77%

17.26 %

23.43 %

67.35 %

18.72 %

-1

0.40%

2 T15cm_R f)

b)

46.43 %

11.58 %

GWTD_ME 3.60% 17.35 %

0.43% s def c fi Ψa (8) sadc (2) others

430

Fig. 6 Relative importance for parameters to R2 a)-i) and ME j)-r) of soil temperature and soil water at 4

431

depths (5, 15, 25, 35 cm) as well as groundwater at site Yonglian. Parameters shown in each sub-figure

432

are the most important parameter from each group, i.e. energy balance, soil heat, soil water, soil salt, then

433

the other parameters.

434

!! At site Yonglian, r!,!"# is shown to be the most important parameter to soil temperature R2 at 4 depths

435

(Fig. 6 a)-d)). The other important parameters were related to soil frost and soil water characteristics (e.g.

436

𝛼, 𝑑! , 𝐶!" , 𝜓! ). For soil total water content and groundwater table depth R2, the important parameters

437

from different groups were also important to soil temperature R2. We can see that except for 𝜓! at various 23


438

depths, the most important parameters were related to energy balance and soil heat transport in frozen

439

!! soils (e.g. 𝑘𝐵 !! , 𝑟!,!"# , 𝑑! , 𝐶!" , 𝛼! ) (Fig 6 e)-i)). For soil temperature ME (Fig. 6 j)-m)), the same

440

parameters were shown important as soil temperature R2. For soil total water content and groundwater

441

table depth ME (Fig. 6 n)-r)), the most important parameters were 𝑠!"# , 𝑑! and 𝜓! from different soil

442

depths. 𝑠!"# is the maximum soil surface water deficit for calculation of surface water balance and

443

adjusting soil surface vapour pressure. It determines the estimate of soil evaporation. The great

444

importance of 𝑠!"# to soil water ME indicated that at site Yonglian, soil evaporation is important in soil

445

water transport.

446

Soil salt related parameters did not show that great importance (around 1% relative importance) to soil

447

temperature and soil water at two sites. Even we have developed a new relationship between osmotic

448

potential and soil freezing temperature and it has shown to be able to improve model performance on

449

simulation of soil temperature, the parameter 𝑠𝑐 did not show great importance at two sites. This

450

indicated that for two sites, 𝑠𝑐 could be assigned as fixed values for different types of salt. We only

451

noticed the adsorption coefficients of salt at various layers show some importance to soil temperature and

452

water. This was because they determine the osmotic potential of soil water and thus impact soil heat and

453

water transport simulation.

454

4.3 Prior and posterior parameters

455

In Table 3, the important parameters and their posterior ranges at two sites are depicted. The posterior

456

!! mean value of 𝑟!,!"# was reduced to 1/3 of prior mean value, and mean value for 𝑑! was also reduced

457

from prior at site Qianguo. The Rratio (range ratio, defined as the posterior range width ratio to prior range

458

!! width) for 𝑟!,!"# and 𝑑! was 0.12 and 0.18, respectively for site Yonglian (Table 3). Parameters

459

𝑧!!,!"#$ , 𝑎!"!"# and 𝐶!" at site Yonglian had larger posterior mean values than prior, and the Rratio was

460

0.54 and 0.68, respectively. Parameters 𝜓! (1) to 𝜓! (3) at site Yonglian also obtained generally larger

461

posterior mean values after calibration, with Rratio of 0.18 to 0.50. 24


462

Table 3 Important parameters and their accepted ranges at site Qianguo and Yonglian.

Posterior values Parameters

Explanation Minimum

Minimum turbulent exchange b coefficient for bare soil in Equation 0.51(0.01) 0.57(0.04) (A18) (Jordan, 1991) Fraction of unfrozen water to wilting point when soil temperature is at -5 oC 0.40(0.23) 0.48(0.45) 𝑑! in Equation (16) Maximum frozen soil thermal 𝐶!" conductivity damping coefficient in 0.67(0.80) 0.87(0.89) Equation (A12) Momentum roughness length of snow 𝑧!!,!"#$ 0.02 0.04 (m) in Equation (A16) Matric water adsorption coefficient for 2.78 9.55 𝑎!"#$% calculation of 𝑠!"# in Equation (A2) Adsorption coefficient of salt in (0.04) (0.50) 𝑠!"# (1) Equation (11) Adsorption coefficient of salt in (0.02) (0.49) 𝑠!"# (2) Equation (11) Adsorption coefficient of salt in (0.10) (0.50) 𝑠!"# (3) Equation (4) Adsorption coefficient of salt in (0.01) (0.48) 𝑠!"# (4) Equation (4) Air entry value of soil (%) in Brooks & 38.34(30.94) 89.91(97.24) 𝜓! (1) Corey equation in Equation (A3) Air entry value of soil (%) in Brooks & 26.49(15.94) 97.00(93.72) 𝜓! (2) Corey equation in Equation (A3) Air entry value of soil (%) in Brooks & 40.83(30.60) 92.27(99.02) 𝜓! (3) Corey equation in Equation (A3) Air entry value of soil (%) in Brooks & (27.33) (63.93) 𝜓! (4) Corey equation in Equation (A3) a Rratio ratio of posterior parameter range to prior parameter range b value without brackets is for site Qianguo, value with brackets is for site Yonglian !! 𝑟!,!"#

463 464 465 466

Maximum

Accepted runs mean

a

Rratio

0.54(0.02)

0.12(0.58)

0.43(0.34)

0.18(0.39)

0.76(0.86)

0.52(0.22)

0.03

0.54

6.36

0.68

(0.24)

(0.93)

(0.21)

(0.91)

(0.33)

(0.74)

(0.24)

(0.76)

57.71(65.12)

0.46(0.81)

80.36(48.49)

0.18(0.78)

68.83(64.46)

0.50(0.66)

(41.18)

(0.36)

For 𝐶!" at site Yonglian, the Rratio was 0.22, much smaller than at site Qianguo (0.52). Rratio of 𝑑! at

467

!! site Yonglian was 0.39, larger than at site Qianguo (0.18). Parameter 𝑟!,!"# at site Yonglian showed

468

totally different Rratio and posterior mean values from site Qianguo, with Rratio of 0.58 and posterior mean

469

!! value of 0.02, respectively. As discussed above, 𝐶!" , 𝑑! and 𝑟!,!"# were important parameters at both

470

sites. They controlled soil heat and energy balance and can influence soil freezing/thawing. Salt

471

adsorption coefficient 𝑠!"# at four depths did not show large changes between posterior and prior

25


472

distributions, with Rratio from 0.74 to 0.93. The Rratio of 𝜓! from four depths at site Yonglian varied from

473

0.36 to 0.81. The large differences in posterior ranges of these parameters indicated these two sites have

474

different surface water and energy balance situations. Site Qianguo is more humid in winter and has more

475

snow events, while site Yonglian has very dry winter but more salt influences on freezing/thawing due to

476

higher salinity at this site. At site Qianguo, parameters such as 𝑧!!,!"#$ and 𝑎!"#$% also showed to be

477

important, and 𝑠!"# at various depths at site Yonglian were shown to be very sensitive.

478

4.4 Soil temperature and water

479

At site Qianguo, soil temperature and soil liquid water content were measured manually at daily

480

resolution due to difficulties in installing automatic measurement instruments at farmers’ land. Accepted

481

simulations generally can capture soil temperature and water dynamics and can cover the observations

482

within their ranges (Fig. 7 a)-b)). After calibration, the mean value of R2 for soil temperature and soil

483

liquid water content at 5 cm depth was 0.87 and 0.31, respectively. Meanwhile, the mean values of ME

484

for soil temperature and soil liquid water content at 5 cm depth was -0.41 oC and -4.89%, respectively.

485

At site Yonglian, hourly soil temperature was obtained in calibration, and achieved high R2 for soil

486

temperature, with mean R2 of 0.90 at 5 cm depth. However, soil temperature was underestimated from

487

end of November to middle of January (Fig. 7 c)). This was mainly due to ice coverage at site Yonglian

488

during this period. After flooding irrigation at the beginning of November, water ponding in the field (~10

489

cm water) was rapidly frozen and kept covering soil surface until middle of January. For this period, ice

490

coverage disturbed water and energy balance at the site Yonglian. Even the snowpack was considered at

491

site Yonglian and a detailed scheme for snow water and energy balance was illustrated in CoupModel, it

492

obviously cannot describe ice coverage in our case. In the future development of the CoupModel, we

493

recommended inclusion of a new scheme for water and energy balance on ice coverage.

26


494

Fig. 7 Comparison of soil temperature and soil water at 5 cm depth at two sites. a)-b) at site Qianguo, c)-d)

495

at site Yonglian. Red line for mean of behavioral simulations, grey lines for simulated mean values +/-

496

standard deviation (sigma), error bar in d) for standard deviation of observations from various plots.

497

Due to failure of TDR in measuring water in salinized frozen soil, we only sampled total water content

498

at site Yonglian. Soil total water content at 5 cm depth had good performance with mean R2 from

499

accepted simulations of 0.80. Even with only 14 sampling dates from each of five plots were selected, the

500

calibrated model can capture soil water dynamics well. Nevertheless, we also noticed large variations in

501

measured total water content from different plots, as indicated by error bars in Fig. 7 d). In the future

502

development of soil water measurement methods, it is necessary to introduce more accurate measurement

503

methods for soil water in saline frozen soils in order to obtain consistent observations of soil water

504

dynamics during winter.

505

4.5 Model validation on water and salt storage

506

Comparison of simulated water storage with measured water storage at different soil depths is depicted

507

in Fig. 8. Results indicated that CoupModel could predict water process well in upper 40 cm soil layer,

508

but some large deviations mainly occurred for 40 to 100 cm at two sites between simulated and observed

509

soil water storages. This was because the accepted simulations was derived by constraining model

510

performance for variables (soil temperature and soil water) in upper 40 cm soil layer, and the data from

511

40-100 cm depth was not used for calibration. This indicated that there might be some unforeseen 27


512

processes in the lower soil layer, and they would influence water processes in whole soil profile (from

513

surface to groundwater). Since the calibration was focusing on the surface water and energy balance, and

514

the upper layer water process was shown to be well-represented by the model, the more detailed

515

consideration of lower layer water processes exceeded the scope of this study. Further work would

516

include calibration of the model in the whole soil profile with more detailed measurements.

517

Fig. 9 shows the simulated salt storage in comparison with measured salt storage based on measured

518

data at various soil depths. At site Qianguo, the Br- storage was generally overestimated by the model in

519

comparison with measured Br- storage in whole soil profile. The simulated Br- storage showed larger

520

uncertainty than the measured. Similarly, at site Yonglian, the simulated Cl- storage at various layers was

521

larger than measured Cl- storage.

522

523

Fig. 8 Comparison of simulated accumulated water storage with measured accumulated water storage at

524

two sites at various soil depths. a) site Qianguo and b) site Yonglian. X error bar denotes standard

525

deviation of observations from various plots, Y error bar denotes standard deviation of water storage from

526

behavioral simulations.

28


527

The overestimation of Cl-/Br- storage at various depths indicated that the upward movement of salt

528

with water was over-estimated. This might be due to the neglecting of diffusion and expulsion of salt in

529

model. Cary and Mayland (1972) have shown that, the diffusion and expulsion processes in frozen soil

530

actually played important roles in salt transport even though the convection was the major process. This

531

was because when soil was frozen, soil solution concentrated. The concentration of soil solution would

532

increase salt concentration gradient between soil layers. In addition, high salt concentration at low

533

temperature would cause salt expulsion from solution due to low salt saturation (Wang et al., 2016).

534

However, it was difficult to measure the diffusion and expulsion of salt in frozen soil. More detailed

535

experiments on diffusion and expulsion of salt are necessary in study of water, heat and salt coupled

536

transport in frozen soils. Validation of soil water and salt storage more data on salt transport as well as

537

water transport would be of importance in calibration of model, since the water and salt transport

538

processes are tightly coupled.

539

Fig. 9 Comparison of simulated salt (Br- and Cl-) storage with measured at two sites. a) site Qianguo and

540

b) site Yonglian. X error bar denotes standard deviation of observations from various plots, Y error bar

541

denotes standard deviation of salt storage from behavioral simulations.

542

5. Conclusions

29


543

Water, heat and salt migrations are coupled in agricultural field. It is important to understand the

544

mechanisms behind this coupling for better water management in cold arid regions. In this study, water,

545

temperature and salt transport during freezing/thawing was simulated and compared with measurements

546

in two seasonally frozen soils in northern China. Uncertainties in both measurements and model were

547

evaluated using Monte-Carlo sampling method and a newly developed CoupModel including salt

548

influences on soil freezing point. Multiple criteria were applied to different model performance metrics

549

for selection of behavioral simulations in evaluating soil temperature, liquid or total water content and

550

groundwater table. With the new freezing point determination methods, simulated soil temperature

551

performance was improved with respect to mean error (ME), by 16% to 77%. Parameters determining

552

energy balance at soil surface as well as soil freezing characteristics were shown important for modeling

553

!! soil water and heat transport processes in LGM analysis. Parameters such as 𝑟!,!"# , 𝑑! and 𝐶!" had large

554

differences in posterior distributions from prior distributions, with posterior range ratio (Rratio) of 0.12 to

555

0.52 and 0.22 to 0.58 at site Qianguo and site Yonglian, respectively. Calibration of the important

556

parameters has improved model performance a lot, with mean posterior R2 values for soil temperature of

557

0.87 and 0.90, and mean posterior R2 values for soil water (liquid and total) of 0.31 and 0.80, at site

558

Qianguo and Yonglian, respectively. Validating of the calibrated model results against soil water and salt

559

storages at different depths has shown that soil water storage was well represented at upper soil layers

560

form surface to 40 cm depth, with water storage at 40-100 cm depth at site Qianguo underestimated, and

561

water storage at 40-100 cm depth overestimated. Meanwhile, salt storage at two sites were generally

562

overestimated by the model in the whole 0-100 cm soil profile, mainly due to lack in considering more

563

salt transport processes such as diffusion and expulsion in frozen soils. The study has emphasized that

564

taking influences of salt on freezing point depression into account in CoupModel can improve model

565

performance and reduce modeling uncertainty. But detailed experiments and model development on salt

566

transport mechanism (e.g. diffusion and expulsion of salt in frozen soils) would be very necessary in

567

investigation of salinization and in water management in cold arid agricultural regions.

30


568

Acknowledgements

569

This research was funded by the National Key Research and Development Program of China (Grant Nos.

570

2017YFC0403304, 2016YFC0501304, 2016YFC0400203), Major Program of National Natural Science

571

Foundation of China (Grant Nos. 51790532, 51790533) and Open Foundation of State Key Laboratory of

572

Water Resources and Hydropower Engineering Science (No. 2017NSG02). We would like to thank Ms.

573

Ai’ping Chen and Mr. Yang Xu from the Yichang Experimental Site for supplying the meteorological

574

data of the studied sites. The authors also appreciate Mr. Pengju Yang, Mr. Dacheng Li and Mr. Weixing

575

Quan for helping analyze the soil samples and processing data in laboratory.

576

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577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606

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Wang, K., Wu, M. and Zhang, R.: Water and Solute Fluxes in Soils Undergoing Freezing and Thawing, Soil Science, 181, 193-201, 2016. Watanabe, K., Kito, T., Dun, S., Wu, J.Q., Greer, R.C. and Flury, M.: Water Infiltration into a Frozen Soil with Simultaneous Melting of the Frozen Layer, Vadose Zone Journal, 12, 0, 10.2136/vzj2011.0188, 2013. Wettlaufer, J. and Worster, M.G.: Premelting dynamics, Annu. Rev. Fluid Mech., 38, 427-452, 2006. Williams, P.J.: Unfrozen water content of frozen soils and soil moisture suction, Géotechnique, 14, 231246, 1964. Wu, J., Jansson, P.E., van der Linden, L., Pilegaard, K., Beier, C. and Ibrom, A.: Modelling the decadal trend of ecosystem carbon fluxes demonstrates the important role of functional changes in a temperate deciduous forest, Ecological Modelling, 260, 50-61, 10.1016/j.ecolmodel.2013.03.015, 2013. Wu, M., Huang, J., Wu, J., Tan, X. and Jansson, P.-E.: Experimental study on evaporation from seasonally frozen soils under various water, solute and groundwater conditions in Inner Mongolia, China, 535 http://dx.doi.org/10.1016/j.jhydrol.2016.01.050, 2016a. Wu, M., Jansson, P.-E., Tan, X., Wu, J. and Huang, J.: Constraining parameter uncertainty in simulations of water and heat dynamics in seasonally frozen soil using limited observed data, Water, 8, 64, 2016b. Wu, S., Jansson, P.E. and Zhang, X.: Modelling temperature, moisture and surface heat balance in bare soil under seasonal frost conditions in China, European Journal of Soil Science, 62, 780-796, 2011. Zhang, W., Wang, G., Zhou, J., Liu, G. and Wang, Y.: Simulating the Water-Heat Processes in Permafrost Regions in the Tibetan Plateau Based on CoupModel, Journal of Glaciology and Geocryology, 34, 1099-1109, 2012. Zhou, X., Zhou, J., Kinzelbach, W. and Stauffer, F.: Simultaneous measurement of unfrozen water content and ice content in frozen soil using gamma ray attenuation and TDR, Water Resources Research, 50, 9630-9655, 2014.

686 687

Appendix

688

Table A1 Calibrated parameters with their prior ranges. Model parameters DvapTortuosity AScaleSorption Air Entry(1)Air Entry(8) HighFlowDamp C LowFlowCondI mped MinimumCond

Descriptions

Symbol

Soil water processes calibrated parameters Tortuosity of vapour dvapb

Air entry value of soil (%) Damping coefficient for hydraulic conductivity in high-flow domain (%) Impedance coefficient for hydraulic conductivity in low-flow domain due to ice existence Minimum hydraulic conductivity for

33

a

Equation A1

Prior Min

Max

0.01 0.1 /b0.02

2 10 /b0.1

A3

0.01

100

cθ,i

A5

0.1 /b0.1

80 /b50

cfi

A6

0.1

10

kmin uc

A7

0.0001

0.001

a

Soil matric water adsorption coefficient

c

ascale

A2

ψa


Value SurfPoolMax DrainSpacing DrainLevel EmpGFLevPea k EmpGFlowPeak InitialGroundW ater DrainLevelMin Ballard_Arp Alpha Ballard_Arp Beta Ballard_Arp a CfrozenMaxDa mp AlphaHeatCoef FreezepointFWi

SaltInputConc

Salt concentration from precipitation input (mg L-1)

MaxSurfExcess MaxSurfDeficit RoughLBareSoi lMom RoughLMomSn ow KBMinusOne WindLessExcha ngeSoil MaxSoilConden s KonzelmannCo ef_1 SThermalCond

20 250 -2.5

z1

A10

-1.5

-0.5

q1

A11

5

15

-

-

-1 /b-2.2 -1.5

-0.5 /b-1.8 -0.5

0.1

0.3

10

30

0.4

0.6

0.5

0.9

0.1 /b500

5000 /b5000

0.1

0.5

20 /b800 1 /b0.01 1500 /b500

40 /b1200 10 /b500 2500 /b1000

a

cCl

-

cCldep

-

cClirrig

-

sadc

-

0

0.5

A14

0.5

1.2

A15

0.5

2

A15

-3

-1

A16

1.0E-05

0.05

z0M,snow

A16

0.005 /b0.025

0.05 /b0.05

kB-1

A17

0

2.5

ra,max-1

A18

0.5 /b1.0E-04

1 /b0.05

emax,cond

A19

2/b1

4/b2

rk1

A20

0.15

0.31

a

A21

2.5E-06

1.0E-05

a

Salt concentration from irrigation (mg L-1)

a

Salt adsorption coefficient

Energy balance processes calibrated parameters Coefficient for adjustment of vapor ψeg difference between upper soil and surface Maximum soil surface water excess in sexcess surface water balance estimate (mm) Soil surface maximum water deficit in sdef surface water balance estimate (mm) Momentum roughness length of bare soil a Z0M (m) Momentum roughness length of snow Ratio of momentum and heat roughness length Windless exchange coefficient of bare soil Maximum soil water condensation rate (mm d-1) Konzelmann coefficient for estimate of longwave radiation Snow thermal conductivity coefficient (W

34

A8 A9 A9

Minimum drainage level (m) Soil heat processes calibrated parameters Coefficient for calculation of thermal α A11 conductivity with Ballard & Arp method Coefficient for calculation of thermal β A11 conductivity with Ballard & Arp method Coefficient for calculation of thermal a A11 conductivity with Ballard & Arp method Maximum damping coefficient of frozen Cmd A12 soil thermal conductivity Heat transfer coefficient for re-freezing of a αh A13 water in high-flow domain (W m-1 oC-1) Coefficient for determining liquid water d1 Equation(16) content when soil is frozen at -5 oC Soil salt processes calibrated parameters Initial salt concentration (mg L-1)

EquilAdjustPsi

wpmax dp zp

/b1.0E05 100 300 -2

Initial groundwater table depth (m)

SaltInitConc

SaltIrrigationCo nc Ad_c(1)Ad_c(16)

/b1.0E-06

determining hydraulic conductivity change with soil temperature (mm d-1) Maximum soil surface pool (mm) Distance between two drainage tubes (m) Initial drainage level (m) Empirical groundwater level peak value (m) Empirical groundwater flow peak value (m)

a

sk


m5 oC-1 kg-2)

Coef

/b1.0E-06

Exponential coefficient for estimate of soil ka A22 0.5 albedo AlbSnowMin Minimum snow albedo amin A23 30 a This parameter was sampled using stochastic log distribution, the others using stochastic linear distribution b Range specific for site Yonglian c Equation is corresponded to the number in Table A2 or in main text AlbedoKExp

689 690 691 692 693

/b1.0E05 1.5 50

Table A2 Calibrated parameters related equations and their descriptions in CoupModel. Equation no.

Equations

Descriptions

Soil water processes Dv = d vapb f a D0

𝑇 + 273.15 !.!" 273.15 𝑀!"#$% 𝑒! 𝑐! = 𝑅(𝑇 + 273.15)

𝐷! =

!!!!"#$% !!

A1

A2

A3

𝑒! = 𝑒! 𝑒 !(!!!"#.!") where f a is the fraction of air-filled pores, D0 is the diffusion coefficient in free air (m2 s-1) and d vapb is a parameter accounting for tortuosity and the enhancement of vapor transfer observed in measurements compared with theory, 𝜓 is matric potential (m, with positive value), 𝑀!"#$% is mole mass of water (18 g mol-1), 𝑅 is gas constant, 𝑒! is saturated vapor pressure (m), 𝑇 is soil temperature (K). Smat = ascale ar kmat pF where kmat is matric hydraulic conductivity (m s-1), ar is the ratio between compartment thickness, Δz , and the unit horizontal area represented by the model, pF is log10 ψ , ascale is an empirical scaling coefficient accounting for the geometry of aggregates. ⎛ψ ⎞ Se = ⎜ ⎟ ⎝ψ a ⎠

-λ

where ψ a is the air-entry tension (m), λ is the pore size distribution index and

Se the effective saturation. (!!!!!/!)

A4

where𝑘!"#

∗ 𝑘! = 𝑘!"# 𝑆! is matric hydraulic conductivity (m s-1), λ is the pore size

distribution index,

Se the effective saturation and 𝑛 is tortuosity. k fh = e

A5

−

θi cθ ,i

(k

w

(θtot ) − kw (θlf + θi ))

where kw (θtot ) is hydraulic conductivity for pores saturated with water (m s1

), k w (θlf + θi ) is hydraulic conductivity when water flow in low domain 35

Soil vapor diffusion coefficient

Sorption capacity rate estimation Water retention curve defined by Brooks and Corey (1964) Unsaturated soil hydraulic conductivity calculated by Mualem (1976) equation Hydraulic conductivity in high flow domain


with ice existence (m s-1), θi / cθ ,i is reduced factor, and cθ ,i is impedance factor. −c Q

A6

kwf = 10 fi kw where c fi is impedance factor, and Q is heat quality, as a ratio of ice content to total water content. kw = ( rAOT + rA1TTs ) max(kw* , kminuc )

where rAOT , rA1T (oC-1) and kminuc (m s-1) are parameters. k w is the total hydraulic conductivity (m s-1), as a sum of hydraulic conductivity from matrix and macro pores. *

A7

qsurf = asurf (Wpool − wpmax )

A8

A9

where asurf is an empirical coefficient, Wpool is the total amount of water in the surface pool (m), and wpmax is the maximal amount of water stored on soil surface without causing surface runoff (m). 4𝑘!! (𝑧!"# − 𝑧! ) 8𝑘!! 𝑧! (𝑧!"# − 𝑧! ) 𝑞!" = + 𝑑!! 𝑑!! where 𝑘!! , 𝑘!! are saturated hydraulic conductivities above and below water level (m s-1), respectively; 𝑧! is soil depth below drainage level (m), 𝑧! is drainage depth to soil surface (m), 𝑑! is distance between two drainage tubes. qgr = q1

A10

max ( 0, z1 − zsat ) max ( 0, z2 − zsat ) + q2 z1 z2

where q1 , q2 are maximum and minimum empirical groundwater flow (m s1 ), respectively; z1 and z2 are highest and lowest empirical groundwater level (m), respectively. Soil heat processes 𝐾!"#$ = (𝐾!"# − 𝐾!"# )𝐾𝑒 + 𝐾!"# 𝑎𝐾!"#$% − 𝐾!"# 𝜌! + 𝐾!"# 𝜌! 𝐾!"# = 𝜌! − 1 − 𝑎 𝜌! For unfrozen soils, !.! !!!!",! !!!!"#$,! !!!",!

A11

A12

!!!!",! ! !!!!"# ! ! ! ! !!!"# (!!!!"# )

𝐾𝑒 = 𝜃!"# For frozen or partially frozen soils, !!! 𝐾𝑒 = 𝜃!"# !",! where 𝐾𝑒 is Kersten number (-), 𝜃!"# is saturation (m3 m-3); 𝑉!",! is volumetric fraction of organic matter (-), 𝑉!"#$,! is volumetric fraction of sand (-), 𝑉!",! is volumetric fraction of coarse fragments (-), 𝛼 and 𝛽 are adjustment factor (-), 𝐾!"#$% is solid thermal conductivity (W m-1 oC-1), 𝐾!"# is air thermal conductivity (W m-1 oC-1), 𝜌! is bulk density (kg m-3), 𝜌! is air density (kg m-3), 𝑎 is adjustment factor (-). 𝑅! = 𝑒 !! !! 𝐶!" + (1 − 𝐶!" ) where 𝑐! is soil surface frost adjustment coefficient (oC-1), 𝐶!" is maximum 36

Hydraulic modification for low flow domain Actual unsaturated hydraulic conductivity after temperature correction Surface runoff estimation

Hooghoudt drainage equation

Empirical drainage equation

This is to calculate soil thermal conductivity for frozen and unfrozen conditions (Ballard and Arp, 2005)

This is used to adjustment thermal


frost damping coefficient (-), 𝑇! is surface soil temperature (oC) qfreeze = αh Δz

A13

T Lf

where α h is heat transfer coefficient (W m-1 oC-1), Δz is thickness of soil layer (m), T is soil temperature (oC), L f is the latent heat of freezing (J m3 ). Energy balance processes

conductivity of frozen soil Redistribution of infiltrating water from high flow to low flow domain

⎛ ψ M water gecorr ⎞ ⎜ ⎟ R ( Ts + 273.15) ⎠

esurf = es (Ts )e⎝ ecorr = 10

A14

( −δsurfψ eg )

where es is the vapor pressure (m) at saturation at soil surface temperature Ts (oC), ψ is the soil water tension (m) and g is the gravitational constant (g m-2 s-1), R is the gas constant (J oC-1 mol-1), 𝑀!"#$% is the molar mass of water (18 g mol-1) and ecorr is the empirical correction factor, ψ eg is a parameter and δsurf is a calculated mass balance at the soil surface (m), which is allowed to vary between the parameters sdef and sexcess given in m of water. ⎛ ⎛ sexcess , δ surf (t − 1) + Wpool + ⎞ ⎞ ⎟⎟ δ surf (t ) = max ⎜ sdef , min ⎜

⎜ ( qin − Es − qv , s + idrip ( z1 ) ) Δt ⎟ ⎟ ⎝ ⎠⎠ is the surface water pool (m), qin is the infiltration rate (m s-1),

Vapor pressure at the soil surface

⎜ ⎝

A15

A16

A17

where Wpool

Es is the evaporation rate (m s ), 𝑖!"#$ is drip irrigation rate (m s ), qv , s , is the vapor flow from soil surface to the central point of the uppermost soil layer (m s-1), sdef is maximal surface water deficit (m) and sexcess is maximal surface water excess (m). 1 ⎛z ⎞ ⎛z ⎞ raa = 2 ln ⎜ ref ⎟ ln ⎜ ref ⎟ f ( Rib ) k u ⎝ zOM ⎠ ⎝ zOH ⎠ -1

-1

where u is the wind speed (m s-1) at the reference height, zref (m), Rib is the bulk Richardson number, k is the von Karman constant and zOM and zOH are the surface roughness lengths for momentum and heat, respectively (m). ⎛z ⎞ kB −1 = ln ⎜ OM ⎟ ⎝ zOH ⎠ −1 where kB is a parameter with a default value 0 (implies zOH = zOM ).

A18

A19

!! 1 !! + 𝑟!,!"# 𝑟!! −1 where ra ,max is a parameter for a upper limit of the aerodynamic resistance in extreme stable conditions. Es = max ( −emax,cond , Lv Es / Lv ) f bare

𝑟!! =

where emax,cond is maximum condensation rate (m s-1) for upmost soil layer to maintain water balance, 𝑓!"#$ is bare soil fraction.

37

Mass balance check at the soil surface

Aerodynamic resistance at stable atmosphere Calculation of of 𝑧!" from kB −1 Aerodynamic resistance in extreme stable conditions Soil evaporation limiting factor


1/4

⎛

ε a,Konzelmann = ⎜ rk1 + rk 2

A20

⎝

⎞ ea ⎟ Ta + 273.15 ⎠

(1 − n ) + r 3 c

3 k3 c

n

o

where ea is vapor pressure (m), 𝑇! is air temperature ( C) nc is cloud fraction; rk 1 , rk 2 , and rk 3 are parameters. 2 ksnow = sk ρ snow

A21

where sk is empirical parameter (W m5 oC-1 kg-2), ρ snow is density of snow (kg m-3). 10

asoil = adry + e − ka

lgψ

( awet − adry )

A22

where adry is albedo of dry soil, awet is albedo of wet soil, and ka is a transform coefficient from wet to dry soil. a S +a T a = a + a e 2 age 3 ∑ a

A23

where amin is minimum albedo of snow, 𝑆!"# is snow age (d), a1 , a2 , and a3 are parameter.

snow

min

1

694 695 696

38

Longwave radiation estimation Thermal conductivity of snow Albedo of bare soil Albedo of snow

Implementation of salt-induced freezing point depression function into

Implementation of salt-induced freezing point depression function into

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